THE EXTENSION OPERATORS ON Bn+1 AND BOUNDED COMPLETE REINHARDT DOMAINS

doi:10.1007/s10473-020-0508-8

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (5): 1271-1288.doi: 10.1007/s10473-020-0508-8

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THE EXTENSION OPERATORS ON Bⁿ⁺¹ AND BOUNDED COMPLETE REINHARDT DOMAINS

Yanyan CUI¹, Chaojun WANG¹, Hao LIU²

1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. Institute of Contemporary Mathematics, Henan University, Kaifeng 475001, China

Received:2019-03-11 Revised:2020-03-27 Online:2020-10-25 Published:2020-11-04
Contact: Yanyan CUI E-mail:cui9907081@163.com
Supported by:
This work was supported by NSF of China (11271359, 11471098), Science and Technology Research Projects of Henan Provincial Education Department (19B110016), Scientific Research Innovation Fund Project of Zhoukou Normal University (ZKNUA201805), Scientific Research Fund of High Level Talents of Zhoukou Normal University (ZKNUC2019004).

Abstract

Abstract: In this article, we extend the well-known Roper-Suffridge operator on $B^{n+1}$ and bounded complete Reinhardt domains in $\mathbb{C}^{n+1}$, then we investigate the properties of the generalized operators. Applying the Loewner theory, we obtain the mappings constructed by the generalized operators that have parametric representation on $B^{n+1}$. In addition, by using the geometric characteristics and the parametric representation of subclasses of spirallike mappings, we conclude that the extended operators preserve the geometric properties of several subclasses of spirallike mappings on $B^{n+1}$ and bounded complete Reinhardt domains in $\mathbb{C}^{n+1}$. The conclusions provide new approaches to construct mappings with special geometric properties in $\mathbb{C}^{n+1}$.

Key words: Roper-Suffridge operator, Reinhardt domains, spirallike mappings

CLC Number:

32A30

Yanyan CUI, Chaojun WANG, Hao LIU. THE EXTENSION OPERATORS ON Bⁿ⁺¹ AND BOUNDED COMPLETE REINHARDT DOMAINS[J].Acta mathematica scientia,Series B, 2020, 40(5): 1271-1288.

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THE EXTENSION OPERATORS ON Bⁿ⁺¹ AND BOUNDED COMPLETE REINHARDT DOMAINS

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